[Paper Review] Broadband Timing and Spectral Study of Accreting Millisecond X-ray Pulsar SAX J1808.4$-$3658 during Its 2022 Outburst

Rahul Sharma, Andrea Sanna+1 more|arXiv (Cornell University)|Feb 12, 2026

Astrophysical Phenomena and Observations0 citations

TL;DR

The paper analyzes simultaneous NICER, NuSTAR, and AstroSat observations of SAX J1808.4–3658 during its 2022 outburst, detailing timing (pulsations, energy dependence, lags) and broadband spectral evolution (soft component, Comptonization, and relativistic reflection) across peak and decay phases.

ABSTRACT

We report on our investigation of the NuSTAR and AstroSat observations along with simultaneous NICER observations of the accreting millisecond X-ray pulsar SAX J1808.4$-$3658, obtained during its tenth outburst from 2022. The NuSTAR observation captured the source near the outburst peak, while AstroSat observed it during the decay phase. Coherent pulsations at $\sim$401 Hz were detected throughout the outburst, with the fundamental amplitude in the 3--30 keV range increasing from $\sim$4% near the peak to $\sim$6% during the decay. The pulsations display strong energy dependence and negative time lags of $\sim$0.2--0.3 ms, with harder photons leading softer ones. The broadband spectra in both epochs are well described by a soft thermal component and Comptonized continuum, together with a prominent relativistic reflection component. As the outburst evolved, the continuum softened ($Γ$ increasing from $\sim$1.88 to $\sim$1.99) and the coronal electron temperature decreased ($kT_{ m e}$ from $\sim$31 to $\sim$18 keV), consistent with enhanced Compton cooling at lower accretion rates. The ionization parameter declined ($\log ξ$ from $\sim$3.4 to $\sim$1.8) while the reflection fraction increased, suggesting a changing accretion geometry with a more compact corona and a larger disk covering fraction during the decay phase. The X-ray luminosity decreased by a factor of $\sim$3 between the two epochs. Our results suggest the coupled evolution of the corona, disk, and magnetosphere as the mass accretion rate declines.

Motivation & Objective

• Investigate timing properties of SAX J1808.4–3658 across two outburst phases (peak and decay) using multi-instrument data.
• Characterize energy-dependent pulse amplitudes and lags to understand emission geometry and propagation effects.
• Model broadband spectra with soft thermal, Comptonized continuum, and relativistic reflection to study accretion physics and disk–corona coupling.
• Examine changes in accretion geometry, ionization, and reflection as the accretion rate declines.
• Cross-compare results with previous outbursts to place the 2022 event in a broader AMXP context.

Proposed method

• Use NuSTAR, AstroSat (LAXPC and SXT), and NICER data for broad energy coverage (0.5–80 keV range).
• Correct photon times for binary motion using updated orbital ephemeris and perform epoch-folding around the known spin frequency (~401 Hz).
• Fit broadband spectra with tbabs*(bbodyrad+nthcomp) and then with tbabs*(bbodyrad+relxillCP) to account for relativistic reflection.
• Jointly fit Epoch 1 and Epoch 2 spectra with shared parameters where appropriate to test for consistency across epochs.
• Extract pulse profiles and energy-resolved fractional amplitudes and time lags for fundamental and harmonic components.
• Incorporate cross-calibration constants among NICER, NuSTAR, and AstroSat instruments and apply systematic uncertainties as needed.

Experimental results

Research questions

• RQ1 What are the pulse timing properties (frequency, amplitude, harmonics) of SAX J1808.4–3658 during the 2022 outburst peak and decay?
• RQ2 How do energy-dependent pulse amplitudes and time lags evolve with decreasing accretion rate?
• RQ3 What does the broadband spectrum (soft component, Comptonization, and reflection) reveal about disk–corona geometry and ionization during peak versus decay?
• RQ4 How does the reflection component and disk ionization evolve as luminosity drops, and what does that imply about accretion geometry?
• RQ5 Are the 2022 observations consistent with prior outbursts in terms of timing and spectral evolution, indicating a common AMXP behavior?

Key findings

Instrument	Spin Frequency (Hz)	Fundamental Amplitude (%)	Harmonic (%)
NuSTAR	400.9752098 (1)	4.06 (11)	1.71 (11)
NICER -1	400.9752096 (1)	4.44 (6)	0.80 (6)
AstroSat	400.9752096 (2)	6.32 (16)	1.72 (16)
NICER -2	400.9752089 (3)	6.54 (7)	0.26 (7)

• Coherent pulsations at ~401 Hz detected throughout both epochs; fundamental amplitude rises from ~4% at peak to ~6% during decay.
• Energy-dependent pulsations show the fundamental amplitude peaking near 3 keV and decreasing at higher energies; a weak harmonic is more prominent at higher energies in the decay epoch.
• Hard photons lead soft ones (negative time lags ~0.2–0.3 ms) for the fundamental in both epochs; harmonic lags are epoch-dependent.
• Broadband spectra require a soft blackbody, a Comptonized component, and a relativistic reflection model; the reflection is linked to disk ionization and geometry changes as the outburst evolves.
• Epoch 1 (peak) to Epoch 2 (decay) shows spectral softening (Γ from ~1.88 to ~1.99) and coronal cooling (kTe from ~31 to ~18 keV) with a luminosity drop by ~3×; ionization parameter logξ decreases from ~3.4 to ~1.8 and reflection fraction increases from ~0.1 to ~0.45.
• These trends suggest a more compact corona and larger disk covering fraction during decay, consistent with coupled evolution of corona, disk, and magnetosphere as accretion rate declines.